Tables Charts S 3 3 Frequency Tables Relative

Tables & Charts S 3. 3 Frequency Tables / Relative Frequency www. mathsrevision. com Cumulative Frequency Table Stem-leaf Diagrams Back to Back Stem Leafs Five Figure Summaries Box Plots Scatter Diagrams 31 -Oct-20 Created by Mr. Lafferty@mathsrevision. com

Starter Questions www. mathsrevision. com S 3. 3 Q 1. Does 5 x 2 – 16 x + 3 factorise to (5 x - 1)(x – 3) Q 2. Change into £’s € 75 exchange rate £ 1 € 1. 5 Q 3. Convert to scientific notation 0. 0675 31 -Oct-20 Created by Mr. Lafferty@mathsrevision. com

Aims of the Lesson www. mathsrevision. com S 3. 3 1. Understand the term Frequency Table and Relative Frequency. 2. Construct a Frequency/Relative Frequency Table. 3. Interpret information from Tables. 31 -Oct-20 Created by Mr. Lafferty 3

Frequency tables Raw data can often appear untidy and difficult to understand. Organising such data into frequency tables can make it much easier to make sense of (interpret) the data. Data Tally Frequency represents a tally of 5 Sum of Tally is the Frequency llll 31 -Oct-20 4

Frequency tables Example 1. A tomato grower ideally wants his tomatoes to have diameters of 60 mm, but a diameter ranging from 58 mm to 62 mm will be acceptable. Organise the diameters given below into a frequency table. 58 56 60 61 56 59 58 58 59 56 60 60 57 59 59 61 60 57 56 62 56 58 59 58 62 60 60 57 62 62 61 62 58 61 56 59 56 58 60 61 58 59 62 59 60 Lowest number 56 Highest number 62 31 -Oct-20 Created by Mr. Lafferty 5

Frequency tables 58 X 57 60 61 56 X 59 58 58 59 X 56 60 60 57 X 59 59 61 Diameter 56 57 60 X 57 59 59 56 X 58 60 58 62 60 59 57 60 59 61 62 Tally ll 58 l l 59 l 60 l 58 61 59 59 60 58 60 61 58 59 62 59 60 Frequency 61 62 31 -Oct-20 Created by Mr. Lafferty 6

58 X X 57 60 X 61 X Frequency Tables Relative 56 59 57 60 56 62 60 58 X 59 X X X X X 60 Frequency X 59 X 62 X X 59 X 57 X 58 X X X 56 59 60 59 61 58 used with always adds 58 60 59 59 61 62 59 X 60 X X X charts X 59 X 60 X X X 59 X Pie up to 1 X 58 57 62 X 61 X 58 X 60 X X 61 X 59 X 58 X X X 59 X 60 Diameter Tally 56 lll 3 Relative Frequency 3 ÷ 48 = 0. 0625 57 llll 4 4 ÷ 48 = 0. 0833 58 59 llll lll 9 13 60 llll 10 9 ÷ 48 = 0. 1875 13 ÷ 48 = 0. 2708 10 ÷ 48 = 0. 2083 61 llll 5 62 llll 4 Total 31 -Oct-20 Frequency 5 ÷ 48 = 0. 1042 4 ÷ 48 = 0. 0833 R 48 Created by Mr. Lafferty 7

Charts & Tables S 3. 3 www. mathsrevision. com Now try Ex 3. 1 Q 2 Ch 6 MIA (page 108) 31 -Oct-20 Created by Mr. Lafferty@mathsrevision. com

Starter Questions www. mathsrevision. com S 3. 3 Q 2. Find the area for the shapes (w - 2) (x – 5) 7 (x – 3) Q 3. Write in standard form 0. 008654 31 -Oct-20 Created by Mr. Lafferty Maths Dept.

Cumulative Frequency Tables www. mathsrevision. com S 3. 3 Learning Intention Success Criteria 1. To explain how to construct a Cumulative Frequency Table. 31 -Oct-20 1. Add a third column to a frequency table to create a Cumulative Frequency Table. Created by Mr. Lafferty Maths Dept.

Cumulative Frequency Tables www. mathsrevision. com S 3. 3 Example : This table shows the number of eggs laid by a clutch of chickens each day over a seven day period. A third column is added to keep a running total (Cumulative Frequency Table). This makes it easier to get the total number of items. You have 1 minute to come up with a question you can easily answer from the table. 31 -Oct-20 Created by Mr. Lafferty Maths Dept. Day Freq. (f) Cum. Freq. Total so far 1 2 2 2 3 5 3 1 6 4 6 12 5 5 17 6 8 25 7 4 29

Cumulative Frequency Tables www. mathsrevision. com S 3. 3 Now try Ex 3. 2 Ch 6 (page 109) 31 -Oct-20 Created by Mr. Lafferty Maths Dept.

Starter Questions S 3. 3 www. mathsrevision. com Q 1. Factorise 4 x 2 + 9 x - 9 Q 2. Multiply out (a) a(ab – a) (b) Q 3. 31 -Oct-20 Created by Mr. Lafferty@mathsrevision. com -2 a( b 2 – a)

Stem Leaf Graphs Construction of Stem-Leaf www. mathsrevision. com S 3. 3 Learning Intention Success Criteria 1. To construct a Stem-Leaf Graph / Dot Graph and answer questions based on it. 1. Construct and understand the Key-Points of a Stem. Leaf Graph / Dot Graphs. 2. Answer questions based on the graph. 31 -Oct-20 Created by Mr. Lafferty Maths Dept.

Stem Leaf Graphs Construction of Stem and Leaf www. mathsrevision. com S 3. 3 A Stem – Leaf graph is another way of displaying information : Ages This stem and leaf graph shows 2 4 6 8 the ages of people waiting in a 3 0 1 3 queue at a post office 4 4 4 5 6 7 9 5 0 3 4 9 How many people in the queue? 20 6 1 4 5 6 How many people in their forties? 6 leaves stem n = 20 Key : 2 4 means 24 31 -Oct-20 Created by Mr. Lafferty Maths Dept.

Stem Leaf Graphs www. mathsrevision. com S 3. 3 We can now answer Construction of Stem and Leaf various questions Example : Construct stem and leaf graph for the following about the adata. weights in (kgs) : Weight (kgs) 1 2 2 3 5 5 2 1 3 9 3 2 2 4 0 0 1 1 12 12 40 13 57 15 54 15 55 21 13 23 55 29 15 32 32 55 40 40 41 21 41 51 32 15 40 54 55 55 55 57 23 41 29 51 12 5 stem 1 4 5 5 5 7 leaves n = 20 Key : 2 3 means 23 31 -Oct-20 Created by Mr. Lafferty Maths Dept.

Dot Plot www. mathsrevision. com S 3. 3 Weight (kgs) We can convert stem leaf into a simple Dot diagram by taking each level and adding a dot for each leaf 1 2 2 3 5 5 2 1 3 9 3 2 2 4 0 0 1 1 5 1 4 5 5 5 7 leaves stem 1 2 3 4 5

Charts & Tables Stem Leaf & Dot Diagram www. mathsrevision. com S 3. 3 Now try Ex 4. 1 Ch 6 (page 112) 31 -Oct-20 Created by Mr. Lafferty Maths Dept.

Starter Questions www. mathsrevision. com S 3. 3 Explain why the statement below are true or false. Factorising x 2 – 9 we get (x - 3) Multiply out 4 x – 2( 8 – x) = 2 x -16 31 -Oct-20 Created by Mr. Lafferty@mathsrevision. com

Stem Leaf Graphs www. mathsrevision. com S 3. 3 Construction of Back to Back Stem-Leaf Learning Intention Success Criteria 1. To construct a Back to Back Stem-Leaf Graph and answer questions based on it. 1. Construct and understand the Key-Points of a Back to Back Stem-Leaf Graph. 2. Answer questions based on the graph. 31 -Oct-20 Created by Mr. Lafferty Maths Dept.

Stem Leaf Graphs Back to Back Stem – Leaf Graphs S 3. 3 www. mathsrevision. com Rugby Team 1 Heights A back to back stem-leaf helps us to compare two sets of data. Write down a question that can be answered easily from the graph. 31 -Oct-20 4 2 1 7 6 8 5 0 6 43 3 1 7 0 n = 15 14 15 16 17 18 Rugby Team 2 Heights 0 3 0 1 1 2 6 7 8 4 1 6 6 4 4 n = 15 14 | 1 represents 141 cm Created by Mr. Lafferty Maths Dept.

Charts & Tables S 3. 3 www. mathsrevision. com Back to Back Stem Leaf Graphs Now try Ex 4. 2 Ch 6 (page 113) 31 -Oct-20 Created by Mr. Lafferty Maths Dept.

Starter Questions www. mathsrevision. com S 3. 3 31 -Oct-20 Created by Mr. Lafferty Maths Dept.

Five Figure Summary www. mathsrevision. com S 3. 3 Learning Intention Success Criteria 1. To explain the meaning and show to workout the five figure summary information for a set of data. 1. Understand the terms L , H, Q 1, Q 2 and Q 3. 2. Be able to work L , H, Q 1, Q 2 and Q 3 For a set of data 31 -Oct-20 Created by Mr. Lafferty Maths Dept.

www. mathsrevision. com S 3. 3 Five Figure Summary When a set of numbers are put in ORDER, it can be summarised by quoting five figures. 1. The highest number (H) 2. The lowest number (L) 3. The median, the number that halves the list (Q 2) 4. The upper quartile, the median of the upper half (Q 3) 5. The lower quartile, the median of the lower half (Q 1)

www. mathsrevision. com S 3. 3 Five Figure Summary Q 1 = lower middle value Find Example Q 2 = Median (middle value) Q 3 = upper summary forvalue the middle the five figure 2, 4, 5, 5, 6, 7, 7, 7, 8, 9, 10 data. The 11 numbers are already in order ! Q 1 = 5 2 4 5 Q 2 = 7 5 6 7 7 L =2 31 -Oct-20 Q 3 = 8 7 8 9 10 H = 10 Created by Mr. Lafferty Maths Dept.

www. mathsrevision. com S 3. 3 Five Figure Summary Q 1 = lower middle value Find Example Q 2 = Median (middle value) Q 3 = upper summary forvalue the middle the five figure 2, 4, 5, 5, 6, 7, 7, 8, 9, 10 data. The 10 numbers are already in order ! Q 1 = 5 2 4 5 Q 2 = 6. 5 5 6 Q 3 = 8 7 7 L =2 31 -Oct-20 8 9 10 H = 10 Created by Mr. Lafferty Maths Dept.

www. mathsrevision. com S 3. 3 Five Figure Summary Q 1 = lower middle value Find Example Q 2 = Median (middle value) Q 3 = upper summary forvalue the middle the five figure 2, 4, 5, 5, 6, 7, 8, 9, 10 data. The 9 numbers are already in order ! Q 1 = 4. 5 2 4 5 Q 2 = 6 5 6 Q 3 = 8. 5 7 8 L =2 31 -Oct-20 9 10 H = 10 Created by Mr. Lafferty Maths Dept.

Five Figure Summary www. mathsrevision. com S 3. 3 Now try Ex 5. 1 Ch 6 (page 115) 31 -Oct-20 Created by Mr. Lafferty Maths Dept.

Starter Questions www. mathsrevision. com S 3. 3 Q 2. Find the area of the first shape and the perimeter of the second shape. (p - 2) (y – 5) 9 31 -Oct-20 Created by Mr. Lafferty Maths Dept. 3

Box Plot www. mathsrevision. com S 3. 3 Learning Intention Success Criteria 1. To show to construct a box plot using the five figure summary. 31 -Oct-20 1. Be able to construct a box plot using the five figure summary data. Created by Mr. Lafferty Maths Dept.

Finding the median, quartiles and inter-quartile range. Example 1: Find the median and quartiles for the data below. 12, 6, 4, 9, 8, 5, 9, 8, 10 Order the data Q 2 Q 1 4, 5, 6, Lower Quartile = 5½ 8, Q 3 8, Median = 8 9, 9, 10, Upper Quartile = 9 Inter- Quartile Range = 9 - 5½ = 3½ 12

Finding the median, quartiles and inter-quartile range. Example 2: Find the median and quartiles for the data below. 6, 3, 9, 8, 4, 10, 8, 4, 15, 8, 10 Order the data Q 2 Q 1 3, 4, 6, Lower Quartile = 4 8, Median = 8 Q 3 8, 9, 10, Upper Quartile = 10 Inter- Quartile Range = 10 - 4 = 6 15,

Box and Whisker Diagrams. Box plots are useful for comparing two or more sets of data like that shown below for heights of boys and girls in a class. Anatomy of a Box and Whisker Diagram. Lower Lowest Quartile Value Whisker 4 5 Median Upper Quartile Whisker Box 6 7 Highest Value 8 9 10 11 12 Boys 130 140 150 160 170 180 cm Girls 190

Drawing a Box Plot. Example 1: Draw a Box plot for the data below Q 2 Q 1 4, 5, 6, 8, Lower Quartile = 5½ 4 5 Q 3 8, 9, Median = 8 6 7 8 9, 10, Upper Quartile = 9 9 10 11 12 12

Drawing a Box Plot. Example 2: Draw a Box plot for the data below Q 2 Q 1 3, 4, 6, 8, Lower Quartile = 4 3 4 5 Q 3 8, 9, 7 8 10, 15, Upper Quartile = 10 Median = 8 6 10, 9 10 11 12 13 14 15

Drawing a Box Plot. Question: Stuart recorded the heights in cm of boys in his class as shown below. Draw a box plot for this data. Q 2 Q 1 Q 3 137, 148, 155, 158, 165, 166, 171, 173, 175, 180, 184, 186 Lower Quartile = 158 130 140 Upper Quartile = 180 Median = 171 150 160 170 180 cm 190

Drawing a Box Plot. Question: Gemma recorded the heights in cm of girls in the same class and constructed a box plot from the data. The box plots for both boys and girls are shown below. Use the box plots to choose some correct statements comparing heights of boys and girls in the class. Justify your answers. Boys 130 140 150 160 170 180 cm Girls 1. The girls are taller on average. 2. The boys are taller on average. 3. The girls show less variability in height. 4. The smallest person is a girl 5. The boys show less variability in height. 6. The tallest person is a boy 190

Box Plot www. mathsrevision. com S 3. 3 Now try Ex 6. 1 Ch 6 (page 117) 31 -Oct-20 Created by Mr. Lafferty Maths Dept.

Starter Questions www. mathsrevision. com S 3. 3 31 -Oct-20 Created by Mr. Lafferty Maths Dept.

Scattergraphs www. mathsrevision. com S 3. 3 Construction of Scattergraphs Learning Intention Success Criteria 1. To construct a scattergraph and answer questions based on it. 1. Construct and understand the Key-Points of a scattergraph. 2. Know the term positive and negative correlation. 31 -Oct-20 Created by Mr. Lafferty Maths Dept.

Write down height and Scattergraphs weight of each player. Construction of Scattergraph www. mathsrevision. com S 3. 3 This scattergraph shows the heights and weights of a sevens football team Bob Tim Sam Joe Gary Jim 31 -Oct-20 Created by Mr. Lafferty Maths Dept. Dave

Scattergraphs S 3. 3 Construction of Scattergraph www. mathsrevision. com When two quantities are strongly connected we say there is a strong correlation between them. Best fit line x x x Strong positive correlation 31 -Oct-20 x x x Best fit line Strong negative correlation Created by Mr. Lafferty Maths Dept.

Draw in the best fit line Scattergraphs www. mathsrevision. com S 3. 3 Construction of Scattergraph Car Price Age (£ 1000) 1 1 9 8 2 3 3 3 4 4 5 8 7 6 5 5 4 2 31 -Oct-20 St ro ng ne ga t ive co r Is there a correlation? If yes, what kind? re Created by Mr. Lafferty Maths Dept. lat ion

Scattergraphs S 3. 3 www. mathsrevision. com Construction of Scattergraphs Now try Ex 7. 1 Ch 6 (page 120) 31 -Oct-20 Created by Mr. Lafferty Maths Dept.